Global attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps

2022/09/22 by Zhanyuan Hou, Hou, Zhanyuan
Mathematics · Medicine · #37C70 #37E30 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Primary: 37C29 #Secondary: 37C65

paper · pdf · doi:10.48550/arxiv.2209.11132

openalex publication_date 2022/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

There is a recent development in the carrying simplex theory for competitive maps: under some weaker conditions a map has a modified carrying simplex (one of the author's latest publications). In this paper, as one of the applications of the modified carrying simplex theory, a criterion is established for a three dimensional Kolmogorov map to have a globally repelling (attracting) heteroclinic limit cycle. As a concrete example, a discrete competitive model is investigated to illustrate the above criteria for global repulsion (attraction) of a hetericlinic limit cycle.

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